Pre-COIE (Earth-One) Superman thought of himself as a Kryptonian first, and an Earthman second. His Kryptonian heritage was of central importance to him, and he identified with that heritage foremost. Pre-COIE Superman thought of himself as a visitor and "resident alien" on Earth.
Post-COIE Superman thought of himself as an Earthman first and a Kryptonian second. He valued his Kryptonian heritage, but it took a secondary position to his upbringing on Earth. Post-COIE Superman saw himself as a full citizen of Earth, not a mere visitor or resident alien.
Where does New 52 Superman stand on this matter?
Buried Alien (The Fastest Post Alive!)